Related papers: Probability density function (PDF) models for part…
Functionals of particles' paths have diverse applications in physics, mathematics, hydrology, economics, and other fields. Under the framework of continuous time random walk (CTRW), the governing equations for the probability density…
In gravel-bed rivers, bedload transport exhibits considerable variability in time and space. Recently, stochastic bedload transport theories have been developed to address the mechanisms and effects of bedload transport fluctuations.…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of whether the flow is turbulent or laminar, the particle dynamics…
The statistical properties of the $E \times B$ flux in different types of plasma turbulence simulations are investigated using probability density distribution functions (PDF). The physics included in the models ranges from two dimensional…
Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
The Lagrangian probability-density-function model, proposed in Part I for dense particle-laden turbulent flows, is validated here against Eulerian-Lagrangian direct numerical simulation (EL) data for different homogeneous flows, namely…
We study the one-point probability distribution functions (PDFs) of the peculiar velocity and the density fluctuation in a cosmological fluid. Within the perturbative approach to the structure formation scenario, the effect of ``pressure''…
Container ships encounter large roll angles and high acceleration, and container loss remains a problem. This study proposes a method for calculating the probability density function~(PDF) of roll angular and cargo lateral accelerations.…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into…
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as…
We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional MHD (see Porth et al. (2014) for details) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter…
We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations…
Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state…
Plasma density fluctuations in the edge plasma of the RFX-mod device are measured through the Gas Puffing Imaging Diagnostics. Statistical features of the signal are quantified in terms of the Probability Distribution Function (PDF), and…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by…